This thesis considers the problem of computing controllers for multivariable systems. System representation is in terms of polynomial matrices and two algorithms are presented which are shown to be useful in the design of controllers for such systems. These algorithms are: i) Factorization of a polynomial matrix, and ii) Computation of a unimodular matrix U satisfying the relation [A B]U = I 1, where A and B are left coprime polynomial matrices. These algorithms do not involve numerically unsatisfactory Euclidean type operations. It is shown that the two algorithms can be used to compute solutions to the system stabilization problem and to the model matching problem. The Regulator Problem with Internal Stability (RPIS) is also discussed, and under certain assumptions it is shown how solutions can be computed.